There are many points in Earth’s history where the Earth System is hypothesised to pass a ‘tipping point’ beyond which a rapid transition to a new and very different state occurs. These critical transitions are common in other complex dynamical systems and are often preceded in datasets by ‘early warning signals’ (EWS) such as critical slowing down (i.e. the system’s recovery time in response to perturbations slows down) and increasing variability (as the data gradually contains more extreme values). Several earlier studies found that EWS can be detected prior to several past climate shifts, suggesting that critical transitions can successfully be detected in the palaeorecord and that palaeo tipping points can be identified. However, doubts have been raised about the reliability of EWS analysis on palaeoclimate records, the degree to which parameter selection can affect the results, and the risk of committing the ‘prosecutor’s fallacy’ when analysing suspected critical transitions. A pilot study analysing the highest-resolution palaeorecords across a number of perturbations to the Cenozoic carbon-climate system found some promising results even when using a cautious approach to counter potential problems. RECOVER focuses on studying these most promising events with additional analytical techniques and data.